Self-Adaptive Inversion Mutation for Combinatorial Representations

Inversion mutation is a typical genetic operator for combinatorial problems like the traveling salesman problem (TSP). It reverses the tour between two randomly chosen cities. Here, we propose a self-adaptive variant of inversion mutation. Self-adaptation is a successful control technique for the mutation strength. Up to now, the concept of self-adaptation has not been applied to inversion mutation. As the number of successive inversion mutation operator applications can be seen as the mutation strength, we propose to control this parameter selfadaptively. In this paper we introduce a self-adaptive variant of inversion mutation (SA-INV). We prove the convergence of inversion mutation and its self-adaptive variant and show experimentally that SA-INV speeds up the evolutionary process, in particular at the beginning of the search. Later, we encounter the strategy bound problem and introduce a heuristic to remain efficient in later search phases.